FUNCTION: weakly_nonneg - test a unitform for weak non-negativity

CALLING SEQUENCE:
weakly_nonneg(q)
weakly_nonneg(q,a1,a2,a3)

PARAMETERS:
q - a unit form
a1, a2, a3 - optional parameters evaluating to a name

SYNOPSIS:

• weakly_nonneg tests, using an algorithm of J.A de la Pena and A. Dean, whether the unit form q given as first argument is weakly non-negative.

• In case q is weakly non-negative the first optional argument will contain the 1-roots and the second optional argument will contain the 0-roots constructed by the algorithm used. A possible third optional argument will be left untouched.

• In case q is not weakly non-negative, the last of the optional arguments will return a vector v with non-negative entries and q(v)<0. The other optional arguments (if there are any) will contain the lists of the 1-roots and the 0-roots constructed by the algorithm.

EXAMPLES:

> a:=hypercritical_algd(4,1);

> q:=titsform(a);

> weakly_nonneg(q,'a1','a2','a3');

> print(a3);

> weakly_nonneg(q,'v');

> print(v);

> 1/2*innerprod(v,q,v);